R A N D O M    M A T R I X    T H E O R Y,    S P R I N G  2 0 1 5

Lectures: Tuesday, 1.25pm-3.15pm, in Warren Weaver Hall 1302.

Lecturer: Paul Bourgade. For office hours, you can set up an appointment or just drop by (Warren Weaver Hall 603).

Course description: This course will introduce techniques to understand the spectrum and eigenvectors of large random self-adjoint matrices, on both global and local scales. Topics include Gaussian ensembles, Dyson's Brownian motion, determinantal processes, bulk and edge scaling limits, universality for random matrices.

Prerequisites: Basic knowledge of linear algebra, probability theory and stochastic calculus is required.

Textbooks: There is no reference book for this course. Possible useful texts are:

Greg Anderson, Alice Guionnet and Ofer Zeitouni. An Introduction to Random Matrices.
Percy Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach.
Percy Deift and Dimitri Gioev, Random Matrix Theory: Invariant Ensembles and Universality.
Laszlo Erdos, lecture notes on universality for random matrices and log-gases.

Homework: Once a month.

Grading: Based on problem sets and attendance/participation at lectures.

A tentative schedule for this course is:

Problem sets.